Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Kaygun, Atabey"'
We prove that the Leibniz PROP is isomorphic (as $\Bbbk$-linear categories) to the symmetric crossed presimplicial algebra $\Bbbk[(\Delta^+)^{op} \mathbb{S}]$ where $\Delta^+$ is the skeletal category of finite well-ordered sets with surjections, but
Externí odkaz:
http://arxiv.org/abs/2404.10925
Autor:
Kaya, Haydar Can, Kaygun, Atabey
Using coinduction and restriction functors, we show that the category of simplicial $\Bbbk$-vector spaces and the category of $\Bbbk$-representations of a crossed simplicial group are equivalent after inverting homotopy equivalences. We do this by fi
Externí odkaz:
http://arxiv.org/abs/2402.19291
Autor:
Güzel, İsmail, Kaygun, Atabey
The homological information about a filtered simplicial complex over the poset of positive real numbers is often presented by a barcode which depicts the evolution of the associated Betti numbers. However, there is a wonderfully complex combinatorics
Externí odkaz:
http://arxiv.org/abs/2209.01099
Autor:
Güzel, İsmail, Kaygun, Atabey
Publikováno v:
Concurrency and Computation Practice and Experience, 2023
In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification
Externí odkaz:
http://arxiv.org/abs/2206.03973
Autor:
Kaygun, Atabey, Sütlü, Serkan
Motivated by the fact that the Hopf-cyclic (co)homologies of function algebras over Lie groups and universal enveloping algebras over Lie algebras capture the Lie group and Lie algebra (co)homologies, we hereby upgrade the classical van Est isomorphi
Externí odkaz:
http://arxiv.org/abs/2205.02828
Autor:
Kaygun, Atabey
We show that every Kac-Moody algebra is birationally equivalent to a smash biproduct of two copies of a Weyl algebra together with a polynomial algebra. We also show that the same is true for quantized Kac-Moody algebras where one replaces Weyl algeb
Externí odkaz:
http://arxiv.org/abs/2105.11360
Autor:
Karan, Alperen, Kaygun, Atabey
In this paper, we develop topological data analysis methods for classification tasks on univariate time series. As an application, we perform binary and ternary classification tasks on two public datasets that consist of physiological signals collect
Externí odkaz:
http://arxiv.org/abs/2102.01956
Autor:
Kaygun, Atabey
A finite non-increasing sequence of positive integers $d = (d_1\geq \cdots\geq d_n)$ is called a degree sequence if there is a graph $G = (V,E)$ with $V = \{v_1,\ldots,v_n\}$ and $deg(v_i)=d_i$ for $i=1,\ldots,n$. In that case we say that the graph $
Externí odkaz:
http://arxiv.org/abs/2101.02299
Autor:
Güzel, İsmail, Kaygun, Atabey
Publikováno v:
Computational Statistics 2022
In this article, we define a new non-archimedean metric structure, called cophenetic metric, on persistent homology classes of all degrees. We then show that zeroth persistent homology together with the cophenetic metric and hierarchical clustering a
Externí odkaz:
http://arxiv.org/abs/2012.02655